(quote from Outlines of the Daf)
>>"Question: Ula taught, wherever the Torah believed 1 witness, he is as 2!
Answer: The Mishnah means - 1 witness said that he died, and we permitted her to get married; 1 witness came and said that he did not die - she remains permitted."<<
I saw that the REMA and others don't permit her to marry LECHATHILA - just BEDIEVED - what is the reason for that - the gemara states clearly the halacha (and the RAMBAM is posek the same)
The Rema states the reason for her not getting married is to "prevent the spread of rumors" (Lazus S'fasaim). This is the Halachah of Rav Asi, as recorded in Kesubos 22b.
Dov Zupnik